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The energy landscapes of repeat-containing proteins: topology, cooperativity, and the folding funnels of one-dimensional architectures.

Ferreiro DU, Walczak AM, Komives EA, Wolynes PG - PLoS Comput. Biol. (2008)

Bottom Line: The one-dimensional nature of the model implies there are simple relations for the experimental observables: folding free-energy (DeltaG(water)) and the cooperativity of denaturation (m-value), which do not ordinarily apply for globular proteins.To illustrate the ideas, we present a case-study of a family of tetratricopeptide (TPR) repeat proteins and quantitatively relate the results to the experimentally observed folding transitions.Based on the dramatic effect that single point mutations exert on the experimentally observed folding behavior, we speculate that natural repeat proteins are "poised" at particular ratios of inter- and intra-element interaction energetics that allow them to readily undergo structural transitions in physiologically relevant conditions, which may be intrinsically related to their biological functions.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California, United States of America.

ABSTRACT
Repeat-proteins are made up of near repetitions of 20- to 40-amino acid stretches. These polypeptides usually fold up into non-globular, elongated architectures that are stabilized by the interactions within each repeat and those between adjacent repeats, but that lack contacts between residues distant in sequence. The inherent symmetries both in primary sequence and three-dimensional structure are reflected in a folding landscape that may be analyzed as a quasi-one-dimensional problem. We present a general description of repeat-protein energy landscapes based on a formal Ising-like treatment of the elementary interaction energetics in and between foldons, whose collective ensemble are treated as spin variables. The overall folding properties of a complete "domain" (the stability and cooperativity of the repeating array) can be derived from this microscopic description. The one-dimensional nature of the model implies there are simple relations for the experimental observables: folding free-energy (DeltaG(water)) and the cooperativity of denaturation (m-value), which do not ordinarily apply for globular proteins. We show how the parameters for the "coarse-grained" description in terms of foldon spin variables can be extracted from more detailed folding simulations on perfectly funneled landscapes. To illustrate the ideas, we present a case-study of a family of tetratricopeptide (TPR) repeat proteins and quantitatively relate the results to the experimentally observed folding transitions. Based on the dramatic effect that single point mutations exert on the experimentally observed folding behavior, we speculate that natural repeat proteins are "poised" at particular ratios of inter- and intra-element interaction energetics that allow them to readily undergo structural transitions in physiologically relevant conditions, which may be intrinsically related to their biological functions.

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Effect of mutations on the coarse-grained model.(A) Fraction folded for chemical denaturation as a function of denaturant (x) for proteins of different length. Insert: Relationship between ΔGwater and m-values. (εS = 1.4, εi = 1.5, α = 2, s0 = 2 fixed). (B) Fraction folded for temperature denaturation as a function of T for proteins of different length. Insert: Relationship between Tf and m-values. (εS = 2.1, εi = 0.5, x = 0, s0 = 8). (C) Fraction folded for chemical denaturation as a function of x for proteins with local perturbations in the eighth repeat as specified in the legend. Insert: Relationship between ΔGwater and m-values. (εS = 3.0, εi = 0.5, α = 2, s0 = 1). (D) Fraction folded for temperature denaturation as a function of T for proteins with local perturbations in the eighth repeat specified in the legend. Insert: Relationship between Tf and m-values (εS = 2.5, εi = 1.5, x = 0, s0 = 8).
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pcbi-1000070-g003: Effect of mutations on the coarse-grained model.(A) Fraction folded for chemical denaturation as a function of denaturant (x) for proteins of different length. Insert: Relationship between ΔGwater and m-values. (εS = 1.4, εi = 1.5, α = 2, s0 = 2 fixed). (B) Fraction folded for temperature denaturation as a function of T for proteins of different length. Insert: Relationship between Tf and m-values. (εS = 2.1, εi = 0.5, x = 0, s0 = 8). (C) Fraction folded for chemical denaturation as a function of x for proteins with local perturbations in the eighth repeat as specified in the legend. Insert: Relationship between ΔGwater and m-values. (εS = 3.0, εi = 0.5, α = 2, s0 = 1). (D) Fraction folded for temperature denaturation as a function of T for proteins with local perturbations in the eighth repeat specified in the legend. Insert: Relationship between Tf and m-values (εS = 2.5, εi = 1.5, x = 0, s0 = 8).

Mentions: In contrast to the situation for globular proteins, repeat-based architecture allows large sequence deletions to be made without severely disrupting the overall fold [7],[8]. Such deletions correspond in the present model to a change in N, the number of folding elements. For a translationally invariant model with no end-effects, both the analytical results and the numerical calculations show that larger proteins exhibit both increased stability and cooperativity (Equations 6–7) (Figure 3A and 3B). This pattern directly results from the fact that more elements are present and that they interact with each other in the same way, thus more terms contribute to the correlation function. In the case of chemical denaturations, this results in a constant that leads to a linear m(ΔGwater) function, as is experimentally observed (see below). For thermal denaturations the change in the susceptibility is low for shorter proteins and becomes exponential as N grows.


The energy landscapes of repeat-containing proteins: topology, cooperativity, and the folding funnels of one-dimensional architectures.

Ferreiro DU, Walczak AM, Komives EA, Wolynes PG - PLoS Comput. Biol. (2008)

Effect of mutations on the coarse-grained model.(A) Fraction folded for chemical denaturation as a function of denaturant (x) for proteins of different length. Insert: Relationship between ΔGwater and m-values. (εS = 1.4, εi = 1.5, α = 2, s0 = 2 fixed). (B) Fraction folded for temperature denaturation as a function of T for proteins of different length. Insert: Relationship between Tf and m-values. (εS = 2.1, εi = 0.5, x = 0, s0 = 8). (C) Fraction folded for chemical denaturation as a function of x for proteins with local perturbations in the eighth repeat as specified in the legend. Insert: Relationship between ΔGwater and m-values. (εS = 3.0, εi = 0.5, α = 2, s0 = 1). (D) Fraction folded for temperature denaturation as a function of T for proteins with local perturbations in the eighth repeat specified in the legend. Insert: Relationship between Tf and m-values (εS = 2.5, εi = 1.5, x = 0, s0 = 8).
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2366061&req=5

pcbi-1000070-g003: Effect of mutations on the coarse-grained model.(A) Fraction folded for chemical denaturation as a function of denaturant (x) for proteins of different length. Insert: Relationship between ΔGwater and m-values. (εS = 1.4, εi = 1.5, α = 2, s0 = 2 fixed). (B) Fraction folded for temperature denaturation as a function of T for proteins of different length. Insert: Relationship between Tf and m-values. (εS = 2.1, εi = 0.5, x = 0, s0 = 8). (C) Fraction folded for chemical denaturation as a function of x for proteins with local perturbations in the eighth repeat as specified in the legend. Insert: Relationship between ΔGwater and m-values. (εS = 3.0, εi = 0.5, α = 2, s0 = 1). (D) Fraction folded for temperature denaturation as a function of T for proteins with local perturbations in the eighth repeat specified in the legend. Insert: Relationship between Tf and m-values (εS = 2.5, εi = 1.5, x = 0, s0 = 8).
Mentions: In contrast to the situation for globular proteins, repeat-based architecture allows large sequence deletions to be made without severely disrupting the overall fold [7],[8]. Such deletions correspond in the present model to a change in N, the number of folding elements. For a translationally invariant model with no end-effects, both the analytical results and the numerical calculations show that larger proteins exhibit both increased stability and cooperativity (Equations 6–7) (Figure 3A and 3B). This pattern directly results from the fact that more elements are present and that they interact with each other in the same way, thus more terms contribute to the correlation function. In the case of chemical denaturations, this results in a constant that leads to a linear m(ΔGwater) function, as is experimentally observed (see below). For thermal denaturations the change in the susceptibility is low for shorter proteins and becomes exponential as N grows.

Bottom Line: The one-dimensional nature of the model implies there are simple relations for the experimental observables: folding free-energy (DeltaG(water)) and the cooperativity of denaturation (m-value), which do not ordinarily apply for globular proteins.To illustrate the ideas, we present a case-study of a family of tetratricopeptide (TPR) repeat proteins and quantitatively relate the results to the experimentally observed folding transitions.Based on the dramatic effect that single point mutations exert on the experimentally observed folding behavior, we speculate that natural repeat proteins are "poised" at particular ratios of inter- and intra-element interaction energetics that allow them to readily undergo structural transitions in physiologically relevant conditions, which may be intrinsically related to their biological functions.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California, United States of America.

ABSTRACT
Repeat-proteins are made up of near repetitions of 20- to 40-amino acid stretches. These polypeptides usually fold up into non-globular, elongated architectures that are stabilized by the interactions within each repeat and those between adjacent repeats, but that lack contacts between residues distant in sequence. The inherent symmetries both in primary sequence and three-dimensional structure are reflected in a folding landscape that may be analyzed as a quasi-one-dimensional problem. We present a general description of repeat-protein energy landscapes based on a formal Ising-like treatment of the elementary interaction energetics in and between foldons, whose collective ensemble are treated as spin variables. The overall folding properties of a complete "domain" (the stability and cooperativity of the repeating array) can be derived from this microscopic description. The one-dimensional nature of the model implies there are simple relations for the experimental observables: folding free-energy (DeltaG(water)) and the cooperativity of denaturation (m-value), which do not ordinarily apply for globular proteins. We show how the parameters for the "coarse-grained" description in terms of foldon spin variables can be extracted from more detailed folding simulations on perfectly funneled landscapes. To illustrate the ideas, we present a case-study of a family of tetratricopeptide (TPR) repeat proteins and quantitatively relate the results to the experimentally observed folding transitions. Based on the dramatic effect that single point mutations exert on the experimentally observed folding behavior, we speculate that natural repeat proteins are "poised" at particular ratios of inter- and intra-element interaction energetics that allow them to readily undergo structural transitions in physiologically relevant conditions, which may be intrinsically related to their biological functions.

Show MeSH
Related in: MedlinePlus